Page 295 - MATLAB an introduction with applications

280 ——— MATLAB: An Introduction with Applications

end
V = X – xOld;
[a,b] = goldBracket(@fLine,0.0,h);
[s,fMin] = goldSearch(@fLine,a,b);
X = X + s*V;
% convergence criterion
if sqrt(dot(X–xOld,X–xOld)/n) < tol
xMin = X; nCyc = j; return
end
iMax = 1; dfMax = df(1);
for i = 2:n
if df(i) > dfMax
iMax = i; dfMax = df(i);
end
end
for i = iMax:n–1
u(1:n,i) = u(1:n,i+1);
end
u(1:n,n) = V;
end
error(‘No converge’)

function z = fLine(s)
global X FUNC V
z = feval(FUNC,X+s*V);

Example E5.7: Use Fletcher-Reeves method to locate the minimum of function

2
2
F(x) = 10x + 3 − 10 , x + 2x .
x
1
1
2
2
1
T
Start with [0 0.05] .
Solution:
Global X FUNC DFUNC V
>> FUNC=@fex3_19;DFUNC=@dfex3_19;X=[0,0.5];
>> [xMin,fMin,nCyc]=fletcherReeves
xMin =
–0.6000
–1.0000
fMin =
–0.6000
nCyc =
3